# QM: The Dilation operator

## Homework Statement

Concicer the dilation operator

$D = \vec{r} * \vec{p}$

Compute $[D,\vec{r} ] and [D, \vec{p}]$

## Homework Equations

$p = - i * hbar$

## The Attempt at a Solution

I think the question is really if $[D, \vec{r}]$ commutes

I got this:
$D = \vec{r} * \vec{p}$
$D = x p_x + y p_y + z p_z$

for the x direction:

$[D, r] = [D, x] = [x, x p_x]$

where do i take it from here?